#### Answer

$\dfrac{\dfrac{3}{n}+\dfrac{5}{n^{2}}}{2}=\dfrac{3n+5}{2n^{2}}$

#### Work Step by Step

In order to find the average of $\dfrac{3}{n}$ and $\dfrac{5}{n^{2}}$, find the sum of these two rational expressions and divide it by two. This can be expressed as follows:
$\dfrac{\dfrac{3}{n}+\dfrac{5}{n^{2}}}{2}$
Evaluate the sum indicated in the numerator:
$\dfrac{\dfrac{3}{n}+\dfrac{5}{n^{2}}}{2}=\dfrac{\dfrac{3n+5}{n^{2}}}{2}=...$
Finally, evaluate the division and simplify:
$\dfrac{3n+5}{n^{2}}\div2=\dfrac{3n+5}{2n^{2}}$